Related papers: Estimating the evidence -- a review

In Bayesian statistics, the marginal likelihood, also known as the evidence, is used to evaluate model fit as it quantifies the joint probability of the data under the prior. In contrast, non-Bayesian models are typically compared using…

The goal of this paper is to compare several widely used Bayesian model selection methods in practical model selection problems, highlight their differences and give recommendations about the preferred approaches. We focus on the variable…

This paper describes a Bayesian method for learning causal networks using samples that were selected in a non-random manner from a population of interest. Examples of data obtained by non-random sampling include convenience samples and…

Models for which the likelihood function can be evaluated only up to a parameter-dependent unknown normalising constant, such as Markov random field models, are used widely in computer science, statistical physics, spatial statistics, and…

The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…

Robust Bayesian models are appealing alternatives to standard models, providing protection from data that contains outliers or other departures from the model assumptions. Historically, robust models were mostly developed on a case-by-case…

This paper introduces and reviews some of the principles and methods used in Bayesian reliability. It specifically discusses methods used in the analysis of success/no-success data and then reminds the reader of a simple Monte Carlo…

Challenging research in various fields has driven a wide range of methodological advances in variable selection for regression models with high-dimensional predictors. In comparison, selection of nonlinear functions in models with additive…

In this manuscript, we discuss the substantial importance of Bayesian reasoning in Social Science research. Particularly, we focus on foundational elements to fit models under the Bayesian paradigm. We aim to offer a frame of reference for…

Multilevel linear models allow flexible statistical modelling of complex data with different levels of stratification. Identifying the most appropriate model from the large set of possible candidates is a challenging problem. In the…

This paper explores Bayesian estimation for categorical data, focusing on simple yet effective models that provide a foundation for applying more advanced methods accurately and reliably in real-world applications. We begin by revisiting…

Bayes Factors, the Bayesian tool for hypothesis testing, are receiving increasing attention in the literature. Compared to their frequentist rivals ($p$-values or test statistics), Bayes Factors have the conceptual advantage of providing…

The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…

We introduce equivalence testing procedures for linear regression analyses. Such tests can be very useful for confirming the lack of a meaningful association between a continuous outcome and a continuous or binary predictor. Specifically,…

In the Bayesian paradigm for presenting forensic evidence to court, it is recommended that the weight of the evidence be summarized as a likelihood ratio (LR) between two opposing hypotheses of how the evidence could have been produced.…

We consider Bayesian model selection in generalized linear models that are high-dimensional, with the number of covariates p being large relative to the sample size n, but sparse in that the number of active covariates is small compared to…

A method is presented for performing joint analyses of cosmological datasets, in which the weight assigned to each dataset is determined directly by it own statistical properties. The weights are considered in a Bayesian context as a set of…

We provide an introductory review of Bayesian data analytical methods, with a focus on applications for linguistics, psychology, psycholinguistics, and cognitive science. The empirically oriented researcher will benefit from making Bayesian…

Nonlinear regression analysis is a popular and important tool for scientists and engineers. In this article, we introduce theories and methods of nonlinear regression and its statistical inferences using the frequentist and Bayesian…

Stochastic simulation approaches perform probabilistic inference in Bayesian networks by estimating the probability of an event based on the frequency that the event occurs in a set of simulation trials. This paper describes the evidence…